Finite Group Databasebeta

← #46848264

Subgroups — #46848264

Order 34688.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774595C211yesmaximal, characteristic, complemented
2#31774553C211yesmaximal, characteristic, complemented
3#31774250C211yesmaximal, characteristic, complemented
4#31774241C211yesmaximal, characteristic, complemented
5#31774207C211yesmaximal, characteristic, complemented
6#31774131C211yesmaximal, characteristic, complemented
7#31774127C211yesmaximal, characteristic, complemented
8#31774111C211yesmaximal, characteristic, complemented
9#31774043C211yesmaximal, characteristic, complemented
10#31774038C211yesmaximal, characteristic, complemented
11#31773984C211yesmaximal, characteristic, complemented
12(C22⋊D271)⋊C8C211yesmaximal, characteristic, complemented
13#31773890C211yesmaximal, characteristic, complemented
14C2×#22576083C211yesmaximal, characteristic, complemented
15#481×C271C211yesmaximal, characteristic, complemented
16C2×#16864653C2211yescharacteristic
17C22×Dic542C2211yescharacteristic
18C2×#16864643C2211yescharacteristic
19C2×#16864643C2211yescharacteristic
20C2×#16864639C2211yescharacteristic
21C22×C271⋊C8C2211yescharacteristic
22C2×C8×D271C2211yescharacteristic
23#22576155—21no—
24#22576151C2211yescharacteristic
25#22576147C2211yescharacteristic
26#22576146—21no—
27#22576145—21no—
28#22576140C2211yescharacteristic
29#22576137—21no—
30#22576135C2211yescharacteristic
31#22576134—21no—
32#22576134C2211yescharacteristic
33#22576132—21no—
34#22576125C2211yescharacteristic
35D4×Dic271—21no—
36#22576122C2211yescharacteristic
37C4×C22⋊D271—21no—
38C4×C22⋊D271C2211yescharacteristic
39#22576118C2211yescharacteristic
40#22576093C2211yescharacteristic
41Dic271⋊C8C2211yescharacteristic
42#22576085C2211yescharacteristic
43#22576085C2211yescharacteristic
44#22576083C2211yescharacteristic
45#22576083C2211yescharacteristic
46#22576083C2211yescharacteristic
47#22576083C2211yescharacteristic
48#22576081C2211yescharacteristic
49#22576080C2211yescharacteristic
50(C2×D271)⋊C8C2211yescharacteristic
51C8×Dic271C2211yescharacteristic
52#121×C271C2211yescharacteristic
53C2×C4⋊C4×C271C2211yescharacteristic
54#106×C271C2211yescharacteristic
55#106×C271C2211yescharacteristic
56#102×C271C2211yescharacteristic
57#102×C271C2211yescharacteristic
58C22⋊C8×C271C2211yescharacteristic
59#16864653—22no—
60#16864653—41no—
61C2×Dic542—22no—
62C2×Dic542—21no—
63C2×Dic542—41no—
64C2×Dic542C2311yescharacteristic
65C2×Dic542C2311yescharacteristic
66C2×D1084—21no—
67C2×D1084C2311yescharacteristic
68C2×C22⋊D271—21no—
69C2×C22⋊D271—21no—
70C2×C22⋊D271D411yescharacteristic
71C22×Dic271—21no—
72C22×Dic271—21no—
73C2×C4×D271—21no—
74C2×C4×D271C2311yescharacteristic
75#16864643—22no—
76#16864643—41no—
77#16864639—41no—
78C2×C271⋊C8—41no—
79C2×C271⋊C8C2311yescharacteristic
80C2×C271⋊C8C2311yescharacteristic
81C8×D271—41no—
82C4⋊Dic271—21no—
83C4⋊Dic271—21no—
84C4⋊Dic271C2311yescharacteristic
85Dic271⋊C4—21no—
86Dic271⋊C4—21no—
87Dic271⋊C4D411yescharacteristic
88C22⋊Dic271—21no—
89C22⋊Dic271—21no—
90C22⋊Dic271D411yescharacteristic
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95(C2×D271)⋊C4—21no—
96(C2×D271)⋊C4D411yescharacteristic
97C4×Dic271—21no—
98C4×Dic271—21no—
99C4×Dic271C2311yescharacteristic
100C2×D4×C271—21no—
101C2×D4×C271C2311yescharacteristic
102C22×C4×C271—21no—
103C22×C4×C271C2311yescharacteristic
104C2×C8×C271C2311yescharacteristic
105C2×C8×C271C2311yescharacteristic
106C4⋊C4×C271—21no—
107C4⋊C4×C271C2311yescharacteristic
108C4⋊C4×C271C2311yescharacteristic
109C4⋊C4×C271C2311yescharacteristic
110C22⋊C4×C271—21no—
111C22×D271—21no—
112C22×D271C2×D411yescharacteristic
113Dic542—21no—
114Dic542—21no—
115Dic542—21no—
116Dic542—42no—
117Dic542#4112yes—
118D1084—21no—
119D1084—21no—
120D1084—81no—
121C22⋊D271—22no—
122C22⋊D271—42no—
123C22⋊D271—42no—
124C2×Dic271—21no—
125C2×Dic271—21no—
126C2×Dic271—21no—
127C2×Dic271—42no—
128C2×Dic271—42no—
129C2×Dic271C2×D411yescharacteristic
130C2×Dic271C2×D411yescharacteristic
131C2×Dic271C2×D411yescharacteristic
132C4×D271—21no—
133C4×D271—21no—
134C4×D271—81no—
135C271⋊C8—21no—
136C271⋊C8—21no—
137C23×C271—21no—
138C23×C271C2×D411yescharacteristic
139D4×C271—21no—
140D4×C271—21no—
141D4×C271—42no—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—21no—
146C2×C4×C271—21no—
147C2×C4×C271—81no—
148C2×C4×C271C2×D411yescharacteristic
149C2×C4×C271C2411yescharacteristic
150C8×C271—21no—
151C8×C271—21no—
152C22×C271—21no—
153C22×C271—21no—
154C22×C271—41no—
155C22×C271—41no—
156C22×C271—41no—
157C22×C271#13512yes—
158C22×C271C22×D411yescharacteristic
159C2×D271—21no—
160C2×D271—21no—
161C2×D271—21no—
162C2×D271—41no—
163C2×D271—41no—
164C2×D271—41no—
165C4×C271—21no—
166C4×C271—41no—
167C4×C271—41no—
168C4×C271—41no—
169C4×C271C2×#4111yescharacteristic
170C4×C271H(5,𝔽2)11yescharacteristic
171Dic271—21no—
172Dic271—22no—
173Dic271—21no—
174Dic271—21no—
175Dic271—41no—
176Dic271—41no—
177C2×C271—22no—
178C2×C271—81no—
179C2×C271#54611yescharacteristic
180C2×C271C2×#13511yescharacteristic
181C2×C271#57711yescharacteristic
182D271—41no—
183D271—81no—
184C271#330111yescharacteristic, complemented, Sylow
185#3301—2711nomaximal, Sylow
186#553—2711no—
187#548—2711no—
188#488—2711no—
189#485—2711no—
190#481D27111yescharacteristic, complemented
191#479—2711no—
192#466—2711no—
193#465—2711no—
194#463—2711no—
195#449—2711no—
196#448—2711no—
197C4×SD16—2711no—
198C8×D4—2711no—
199#416—2711no—
200C2×#103—2711no—
201C2×#41—2711no—
202C22×Q8—2711no—
203C2×SD16—2711no—
204C2×SD16—2711no—
205C2×D8—2711no—
206C22×C8—2711no—
207C22×C8—2711no—
208#126—5421no—
209#125—2711no—
210#124—2711no—
211#124—5421no—
212#123—5421no—
213C22⋊Q8—2711no—
214C22⋊Q8—5421no—
215#121—2711no—
216#121—2711no—
217#121—5421no—
218#121—5421no—
219#121C2×D27111yescharacteristic
220C4×Q8—2711no—
221C4×D4—2711no—
222C4×D4—2711no—
223C4×D4—5421no—
224C4×D4—5421no—
225#117—2711no—
226C2×C4⋊C4C2×D27111yescharacteristic
227#107—2711no—
228#106C2×D27111yescharacteristic
229#106C2×D27111yescharacteristic
230C4⋊C8—2711no—
231#103—2711no—
232#103—2711no—
233#103—2711no—
234#103—2711no—
235#103—2711no—
236#103—2711no—
237#102—2711no—
238#102—2711no—
239#102C2×D27111yescharacteristic
240#102C2×D27111yescharacteristic
241C22⋊C8—2711no—
242C22⋊C8C2×D27111yescharacteristic
243C4×C8—2711no—
244#41—5422no—
245#41—10841no—
246C2×Q8—2711no—
247C2×Q8—2711no—
248C2×Q8—5422no—
249C2×Q8—5421no—
250C2×Q8—10841no—
251C2×D4—21no—
252C2×D4—2711no—
253C2×D4—2711no—
254C2×D4—5421no—
255C2×D4—5421no—
256C2×D4—5421no—
257C2×D4C22×D27111yescharacteristic
258C22×C4—21no—
259C22×C4—2711no—
260C22×C4—5421no—
261C22×C4—5421no—
262C22×C4—5421no—
263C22×C4C22×D27111yescharacteristic
264SD16—5422no—
265SD16—10841no—
266D8—10841no—
267C2×C8—2711no—
268C2×C8—2711no—
269C2×C8—10841no—
270C2×C8—10841no—
271C2×C8C22×D27111yescharacteristic
272C2×C8C22×D27111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2711no—
275C4⋊C4—2711no—
276C4⋊C4—5421no—
277C4⋊C4—5421no—
278C4⋊C4—5421no—
279C4⋊C4—5421no—
280C4⋊C4C22×D27111yescharacteristic
281C4⋊C4C22×D27111yescharacteristic
282C4⋊C4C22×D27111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2711no—
285C22⋊C4—2711no—
286C22⋊C4—5421no—
287C22⋊C4—5421no—
288C22⋊C4—5421no—
289C22⋊C4—5421no—
290C22⋊C4—5421no—
291C22⋊C4—5421no—
292C22⋊C4—5421no—
293C42—2711no—
294C42—5421no—
295C42—5421no—
296C23—21no—
297C23—2711no—
298C23—5421no—
299C23D4×D27111yescharacteristic
300Q8—2712no—
301Q8—5421no—
302Q8—5421no—
303Q8—5421no—
304Q8—10842no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—5422no—
309D4—5421no—
310D4—5421no—
311D4—10842no—
312D4—10842no—
313D4—21681no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—2711no—
321C2×C4—2711no—
322C2×C4—2711no—
323C2×C4—5421no—
324C2×C4—5421no—
325C2×C4—5421no—
326C2×C4—5421no—
327C2×C4—5421no—
328C2×C4—10842no—
329C2×C4—10842no—
330C2×C4—21681no—
331C2×C4D4×D27111yescharacteristic
332C2×C4C23×D27111yescharacteristic
333C8—21no—
334C8—21no—
335C8—5421no—
336C8—5421no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—5421no—
343C22—5421no—
344C22—5421no—
345C22—10841no—
346C22—10841no—
347C22—10841no—
348C22#2257618112yes—
349C22C2×D4×D27111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—5421no—
355C4—5422no—
356C4—5421no—
357C4—5421no—
358C4—10841no—
359C4—10841no—
360C4#41×D27111yescharacteristic
361C4#2257620611yescharacteristic
362C2—22no—
363C2—81no—
364C2—10841no—
365C2—21681no—
366C2#3177453911yescharacteristic
367C2C2×#2257618111yescharacteristic
368C2#3177470711yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#481×C271C2
socleC22×C271C22×D4
hypercenter#481D271
hypocenterC271#3301
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #31774595C2semidirect
2. #31774553C2semidirect
3. #31774250C2semidirect
4. #31774241C2semidirect
5. #31774207C2semidirect
6. #31774131C2semidirect
7. #31774127C2semidirect
8. #31774111C2semidirect
9. #31774043C2semidirect
10. #31774038C2semidirect
11. #31773984C2semidirect
12. (C22⋊D271)⋊C8C2semidirect
13. #31773890C2semidirect
14. C2×#22576083C2semidirect
15. #481×C271C2semidirect
184. C271#3301semidirect
190. #481D271semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#317745952
#317745532
#317742502
#317742412
#317742072
#317741312
#317741272
#317741112
#317740432
#317740382
#317739842
(C22⋊D271)⋊C82
#317738902
C2×#225760832
#481×C2712
#3301271